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What is Symmetry And Reciprocity Of Two-Port Networks?

A passive, linear 2-port network is said to be symmetrical if the two ports can be interchanged (that is, the input port is made the output port and the output port is made the input port) without changing the port voltages and currents. The condition of symmetry is conveniently written in terms of z parameters as

z11 = z22

Or V1/I1|I2=0 = V2/I2|I1=0

The conditions of symmetry may also be derived in terms of other parameters. These conditions are given in Table below

Table

Parameters relationships for symmetrical and reciprocal networks

Parameter

Condition of summetry

Condition of reciprocity

Z

z11 = z22

z12 = z21

y

y11 = y12

y12 = y21

h

Δh = 1

h12 = –h21

g

Δg = 1

g12 = –g21

a

A = D

AD – BC = 1

a

a11 = a22

Δa = 1

b

b11 = b22

Δb = 1

A passive linear, 2-port network is said to be reciprocal if reciprocity principle holds. That is,

I1/V1|V1=0 = I2/V2|V2=0

Or y12 = y21

The conditions of reciprocity may also be derived in terms of other parameters. These conditions are given in Table above

Thus, it is seen that a passive, linear reciprocal, 2-port network may be characterized by three z parameters, or three-y parameters. Similarly, three ABCD parameters are sufficient to describe a passive, linear, reciprocal 2-port network. Further if the network is symmetrical (for which A = D), only two parameters are needed to describe the network.

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